Explatory Data Analysis for 2ForcedChoice Modal Experiments

Author

Utku and Sarah

1 Procedure for both experiments

  • Platform and environment
    • The experiments were conducted online in PCIbex (PennController for Ibex). The interface switched to fullscreen at the start of the main task and exited fullscreen at the end.
    • Participants were instructed to use a desktop or laptop with Google Chrome, a keyboard, and a mouse or trackpad in a distraction-free setting.
    • Total session time was approximately 25 minutes.


  • Consent and demographics
    • After an introduction screen, participants viewed and downloaded a consent form and indicated consent to proceed.
    • A brief demographics form collected age, gender, location (state and country), computer type, native language, and other languages.


  • Design and counterbalancing
    • Aim: the experiments tested the interpretive force of must compared to other modal elements, or the absence of a modal.
    • Participants were randomly assigned (between subjects) to one of four answer sets: bare, have to, will, prob (a separate CSV file per set).
    • Experimental, filler, and attention-check trials were fully intermixed and randomized for each participant.
    • On critical trials, the modal from a participant’s assigned set was contrasted with must (for example, will vs. must).
    • Filler trials featured the remaining modal options among the two responses.
    • Attention-check trials consisted of unambiguous deductive contexts to verify attention.
    • Counts: experimental items = X; fillers = X; attention checks = X.
    • Exclusion criterion: participants were excluded if they failed more than 20% of attention-check trials.
    • Each experimental item appeared in one of three context conditions: abductive, deductive, or inference.
    • Context conditions were assigned using a Latin square, so each participant saw exactly one context per item.
    • On every trial, the two response options were order-randomized.


  • Between-experiment differences:
    • Experiment 1 used SONA participants and included preambles that conveyed contextual information in an if-clause.
    • Experiment 2 used Prolific participants and included a shorter preamble consisting only of a well, then… phrase.
    • Experiment 3 used Prolific participants and replicated bare and haveto from Experiment 1
    • Experiment 4 used ‘got to’ constructions with “well then” and “if p ,” contrustions


  • Instructions and practice
    • Participants read step-by-step instructions with two worked examples (one obvious and one less obvious).
    • Additional practice trials followed, using the same two-stage flow as the main task.


  • Trial structure (main task)
    • Context presentation: participants saw a short, three-turn conversation (Speaker A – Speaker B – Speaker A) that provided the relevant context.
    • Dialogue (reading) phase: participants pressed the space bar to advance or were auto-advanced after 120 s. A Dialogue RT (ms) was recorded from dialogue onset to advance.
    • Choice phase: two candidate sentence completions appeared simultaneously. Participants selected the option they judged most appropriate; a 60 s timeout applied. An Answer RT (ms) was recorded from option onset to response.
    • After the response, the screen cleared and the next trial began.


  • Breaks
    • Brief on-screen breaks were inserted at regular intervals (about every four trials). Participants resumed by pressing the space bar.


  • Measures and logging
    • For each trial, the following were logged: item and condition labels (Type, Group, Item, Inference, ConditionName, Condition), the three dialogue lines (D1–D3), both options (A1–A2), the selected answer, Dialogue RT, Answer RT, and TrialNumber.
    • Practice trials were logged with the same structure and marked as practice.


  • Debrief and redirect
    • Upon completion, results were submitted to the server, fullscreen ended, and participants were automatically redirected to a debrief and credit form hosted at UMD or Prolific.

2 Experiment 1

2.1 Participant Accuracy in Check Items

must vs. prob
Total N = 14
Bin Count
[0.5,0.6) 3
[0.7,0.8) 6
[0.9,1] 5
must vs. will
Total N = 6
Bin Count
[0.7,0.8) 1
[0.9,1] 5
haveto vs. must
Total N = 9
Bin Count
[0.7,0.8) 2
[0.9,1] 7
bare vs. must
Total N = 11
Bin Count
[0.9,1] 11
Click to expand Demographics

Mean Age: 22.00 (18–49)

Subject Age Gender Location Computer Language Other language
S[51] 18 Male Maryland, United States of America Mac English Spanish (proficient), Darija (novice)
S[55] 30 Male MD, USA Mac English
S[60] 18 Unlabeled Maryland, United States PC (Lenovo) English Cantonese
S[5] 19 Female Maryland, USA PC English Hindi, Urdu
S[6] 18 Female MD, USA Windows English
S[9] 21 Female Maryland, USA Mac English
S[12] 49 MALE MARYLAND, USA LINUX PC ENGLISH SPANISH, ITALIAN, RUSSIAN NONE FLUENTLY
S[17] 19 Female Maryland, United States Windows Laptop English Spanish
S[21] 18 Male Maryland Laptop English
S[22] 18 Male Maryland, United States PC English
S[26] 18 Female Maryland, USA Lenovo English
S[27] 20 Female Maryland, USA Windows English Mandarin Chinese
S[31] 18 Female College Park, Maryland Mac English
S[34] 24 Female Maryland, United States Mac English Korean

Mean Age: 21.67 (18–36)

Subject Age Gender Location Computer Language Other language
S[53] 18 male maryland, usa pc english
S[57] 18 female Maryland, USA laptop english
S[59] 18 Female Maryland, USA Mac English Spanish
S[10] 21 Male Maryland, Prince George’s County PC English Spanish
S[11] 19 Male Maryland, US Windows English
S[20] 36 Male Baltimore, MD Mac English French, German

Mean Age: 19.00 (18–22)

Subject Age Gender Location Computer Language Other language
S[56] 18 female Maryland, USA lenovo thinkpad english chinese (beginner)
S[58] 19 Female MD, USA Mac English
S[1] 18 Female College Park, Maryland Mac English Cantonese
S[13] 19 Male College Park, MD, USA Mac English Gujarati
S[15] 20 Male College Park, MD Mac English Telugu
S[16] 22 Male MD, USA PC English German
S[28] 18 Female Maryland, USA Mac English Spanish
S[30] 19 Male Maryland, United States of America PC English
S[35] 18 Female College Park, MD Mac English Mandarin Chinese

Mean Age: 21.27 (18–40)

Subject Age Gender Location Computer Language Other language
S[52] 18 male MD, USA Thinkpad X1 Carbon English Mandarin, Spanish, Japanese, Hindi
S[54] 20 Female Maryland, United States PC English
S[3] 20 Male Massachusetts PC English
S[7] 18 woman MD, USA Windows English Japanese
S[8] 40 Female Maryland, USA PC English
S[14] 19 Female Maryland, United States Mac English Vietnamese
S[18] 26 male Maryland, USA PC English Spanish (L2 ~B2/C1)
S[19] 19 Female Maryland, USA PC English Spanish
S[24] 18 Female Maryland, United States Mac English
S[25] 18 female Maryland, USA Dell laptop English Vietnamese
S[32] 18 female MD, United States Mac English

2.2 Answer Choice Summary

We report target-response proportions by inference (a, d, i) and type (must, prob, have to, will, bare). Confidence intervals are Morey–Cousineau, truncated to [0,1].

Per-cell trials and items increase across blocks:

  • prob: n = 10, N = 5
  • will: n = 10, N = 5
  • have to: n = 14, N = 7
  • bare: n = 22, N = 11

Block: prob (n = 10; N = 5)

  • a: prob 0.70 (0.42–0.98) > must 0.30 (0.02–0.58)
  • d: must 0.70 (0.42–0.98) > prob 0.30 (0.02–0.58)
  • i: prob 0.60 (0.17–1.00), must 0.40 (0.00–0.83)

Takeaway: Strong complementarity—prob peaks in a, must in d; i is mixed with wider CIs.

Block: will (n = 10; N = 5)

  • a: must 1.00 (1.00–1.00); all others 0.
  • d: must 0.80 (0.34–1.00); will 0.20 (0.00–0.66)
  • i: must 0.80 (0.52–1.00); will 0.20 (0.00–0.48)

Takeaway: Will is at (or near) floor; must dominates, with a small will share in d/i.

Block: have to (n = 14; N = 7)

  • a: must 0.93 (0.78–1.00); have to 0.07 (0.00–0.22)
  • d: must 0.93 (0.78–1.00); have to 0.07 (0.00–0.22)
  • i: must 0.71 (0.50–0.93); have to 0.29 (0.07–0.50)

Takeaway: Must is clearly preferred; i shows a modest but reliable share for have to.

Block: bare (n = 22; N = 11)

  • a: must 0.86 (0.73–1.00); bare 0.14 (0.00–0.27)
  • d: must 0.91 (0.73–1.00); bare 0.09 (0.00–0.27)
  • i: must 0.86 (0.73–1.00); bare 0.14 (0.00–0.27)

Takeaway: Must overwhelmingly beats bare across all inference conditions; bare shows a small baseline.

2.3 Reading Times Summary

3 Experiment 2

3.1 Participant Accuracy in Check Items

must vs. prob
Total N = 21
Bin Count
[0.5,0.6) 1
[0.9,1] 20
must vs. will
Total N = 21
Bin Count
[0.7,0.8) 1
[0.9,1] 20
haveto vs. must
Total N = 21
Bin Count
[0.9,1] 21
bare vs. must
Total N = 21
Bin Count
[0.7,0.8) 3
[0.9,1] 18
Click to expand Demographics

Mean Age: 45.86 (27–73)

Subject Age Gender Location Computer Language Other language
S[1] 44 male TN, USA HP PC English
S[2] 49 male Michigan, USA PC English
S[3] 46 male texas, USA PC English
S[4] 52 male Tennessee, USA Mac English
S[5] 32 Male NC, USA PC English
S[6] 59 Female Alabama P.C. English
S[7] 73 Female Rhode Island PC English
S[8] 47 Male NY, USA PC English
S[9] 41 male MA, USA PC English
S[10] 48 Woman NY, USA PC English
S[11] 56 male Virginia, USA PC English
S[12] 50 female California, United States laptop English
S[13] 64 Male Illinois, United States PC English
S[14] 30 Female Hawaii, USA PC English
S[15] 34 Female New York, United States of America PC English
S[16] 40 Female New York, USA Laptop English
S[17] 42 Male Kentucky, USA Windows laptop English
S[18] 37 male Indiana, United states PC English
S[19] 27 woman US, TEXAS WINDOWS ENGLISH
S[20] 32 man Tennessee, United States PC English Spanish
S[21] 60 Male North Carolina, United States PC English

Mean Age: 46.10 (26–67)

Subject Age Gender Location Computer Language Other language
S[1] 31 female NJ USA Mac English
S[2] 52 Female Minnesota, USA PC English Beginning Spanish
S[3] 54 Male CA, USA PC English
S[4] 30 Female Kentucky, USA PC English
S[5] 43 female Connecticut, USA PC English
S[6] 26 male north carolina, united states pc english
S[7] 55 female Tennessee, USA Windows Laptop English
S[8] 37 Female Georgia, United States PC English
S[9] 36 female Maryland United states Chromebook English
S[10] 43 Female Texas, USA Mac English
S[11] 67 female Wisconsin, USA PC English Spanish
S[12] 46 male tn, usa PC English
S[13] 49 Female Massachusetts PC English
S[14] 56 female california united states pc english
S[15] 62 male ny, usa pc English
S[16] 51 Female Virginia Laptop English
S[17] 28 Female Maine, USA PC English
S[18] 59 male Tennessee, USA PC English
S[19] 52 female Virginia PC English English
S[20] 29 Female California United States Laptop English
S[21] 62 female Washington, USA PC English

Mean Age: 37.24 (22–71)

Subject Age Gender Location Computer Language Other language
S[1] 24 Male Florida, USA PC English
S[2] 45 Male Oregon, USA PC English
S[3] 29 f fl, usa pc english
S[4] 22 F CO, USA PC ENGLISH
S[5] 32 male Minnesota, USA PC English
S[6] 27 female Georgia, USA PC English
S[7] 38 Female Louisiana, United States PC English
S[8] 33 Woman Maryland, USA Mac English
S[9] 58 Male Georgia, USA PC English
S[10] 45 Male MS, USA MAC English
S[11] 53 Female United States Mac English English
S[12] 35 Non-Binary AFAB MN, USA Mac English
S[13] 42 woman Tennessee, USA PC(windows) English
S[14] 30 Female Indiana, USA PC English
S[15] 41 Female California, USA Mac English
S[16] 28 Male PA, USA Linux English
S[17] 47 Male Michigan, United States PC English
S[18] 71 Female Arizona, United States PC English
S[19] 26 Female Illinois, USA PC English Language
S[20] 25 Woman Delaware PC English
S[21] 31 Male MA, USA Windows English

Mean Age: 43.00 (21–66)

Subject Age Gender Location Computer Language Other language
S[1] 36 male CA, USA PC English
S[2] 35 Male AL, Geneva Chromebook English No others
S[3] 38 male Michigan, United States Of America PC English
S[4] 55 male California, USA PC English
S[5] 51 Male New York, United States PC English
S[6] 61 female California, US PC English
S[7] 21 male Georgia, United States PC English
S[8] 35 male VA, USA windows PC English
S[9] 45 Male Ohio, United States PC English
S[10] 66 Female Florida, United States PC English
S[11] 44 Male GA, USA PC English
S[12] 40 Female Louisiana, United States PC English
S[13] 25 Male United States PC English
S[14] 47 male New York, United States PC English
S[15] 46 Female Nevada, USA PC English
S[16] 47 Female Mississippi, United States PC English
S[17] 43 Woman SC, United States Windows English
S[18] 29 female ohio, USA PC english
S[19] 39 Male United States PC English
S[20] 45 Male Indiana, USA Laptop English
S[21] 55 female NY PC English English

3.2 Answer Choice Summary

We report target-response proportions by inference (a, d, i) and type (must, prob, have to, will, bare). Confidence intervals are Morey–Cousineau, truncated to [0,1].

Per-cell trials and items by block:

  • prob: n ≈ 40, N = 20
  • will: n = 40, N = 20
  • have to: n = 42, N = 21
  • bare: n = 36, N = 18

Block: prob (n ≈ 40; N = 20)

  • a: prob 0.538 (0.385–0.715) > must 0.462 (0.285–0.615)
  • d: must 0.725 (0.581–0.869) > prob 0.275 (0.131–0.419)
  • i: must 0.550 (0.399–0.701), prob 0.450 (0.299–0.601)

Takeaway: Clear complementarity—prob peaks in a, must in d; i is near 50/50.

Block: will (n = 40; N = 20)

  • a: must 0.950 (0.885–1.000); will 0.050 (0.000–0.115)
  • d: must 0.775 (0.631–0.919); will 0.225 (0.081–0.369)
  • i: must 0.900 (0.790–1.000); will 0.100 (0.000–0.210)

Takeaway: Must dominates; will contributes small shares, largest in d.

Block: have to (n = 42; N = 21)

  • a: must 0.929 (0.831–1.000); have to 0.071 (0.000–0.169)
  • d: must 0.714 (0.549–0.880); have to 0.286 (0.120–0.451)
  • i: must 0.905 (0.800–1.000); have to 0.095 (0.000–0.200)

Takeaway: Must is preferred overall; d shows the largest have to share.

Block: bare (n = 36; N = 18)

  • a: must 0.778 (0.604–0.952); bare 0.222 (0.048–0.396)
  • d: must 0.528 (0.334–0.722); bare 0.472 (0.278–0.666)
  • i: must 0.694 (0.539–0.849); bare 0.306 (0.151–0.461)

Takeaway: Unlike Exp 1, bare takes a substantial share—especially in d—though must still leads overall.

3.3 Reading Times Summary

3.4 Age groups

The results does not seem to be a function of age. But there are some mismatches.

4 Experiment 3

4.1 Participant Accuracy in Check Items

haveto vs. must
Total N = 21
Bin Count
[0.9,1] 21
bare vs. must
Total N = 21
Bin Count
[0.7,0.8) 1
[0.9,1] 20
Click to expand Demographics

Mean Age: 48.57 (35–73)

Subject Age Gender Location Computer Language Other language
S[1] 37 male California, USA PC english
S[2] 60 Female Idaho, USA PC English
S[3] 47 MALE BURKETVILLE, MD PC ENGLISH NONE
S[4] 38 male ma, usa mac english
S[5] 60 Female CA, USA Mac English
S[6] 50 Female California, USA Mac English
S[7] 42 female RI, USA PC English
S[8] 73 Female Kansas, USA laptop English
S[9] 35 male Colorado, United States PC English
S[10] 49 Male MN Mac English
S[11] 46 male Washington, USA pc English
S[12] 42 Female Virginia, USA PC English
S[13] 72 female Ohio, United States PC English
S[14] 44 female IL, USA PC English
S[15] 46 Male Michigan, United States PC English
S[16] 52 male CT USA pc English
S[17] 41 male Indiana. United states Laptop English
S[18] 58 female Michigan, United States PC English
S[19] 39 male NH, USA PC English
S[20] 44 female California, US 1pc English
S[21] 45 Male NC, USA PC English French (Intermediate), Spanish (Basic)

Mean Age: 48.52 (36–72)

Subject Age Gender Location Computer Language Other language
S[1] 49 woman NY, USA PC English
S[2] 43 Female New York, US HP English
S[3] 38 Female New York, United States PC English
S[4] 38 Male Arlington, USA PC English English
S[5] 71 Male Texas, United States PC English
S[6] 43 F MA, USA Mac English
S[7] 45 Female Maryland, USA Laptop%2C Windows English
S[8] 37 female La Porte, Texas PC English
S[9] 47 Male Florida, USA PC English
S[10] 52 female Missouri, USA Mac English
S[11] 51 male New Mexico, USA PC English
S[12] 44 Female NJ, United States PC English
S[13] 51 Male Nevada, USA PC English 0
S[14] 48 male OH, USA PC English
S[15] 36 female California, usa pc english
S[16] 72 Female Louisiana, United States PC English
S[17] 57 woman CA USA Mac English
S[18] 51 female michigan pc english
S[19] 60 male Missouri, USA PC American English Patios
S[20] 39 male RI, USA Pc English
S[21] 47 Male PA, USA MAC English

4.2 Answer Choice Summary

We report target-response proportions by inference (a, d, i) and type (must, prob, have to, will, bare). Confidence intervals are Morey–Cousineau, truncated to [0,1].

Per-cell trials and items by block:

  • have to: n = 42, N = 21
  • bare: n = 40, N = 20

Block: have to (n = 42; N = 21)

  • a: must 0.93 (0.86–1.00); have to 0.07 (0.00–0.15)
  • d: must 0.88 (0.77–0.99); have to 0.12 (0.01–0.23)
  • i: must 0.86 (0.76–0.95); have to 0.14 (0.05–0.24)

Takeaway: Must clearly dominates; have to contributes a small but non-zero share, largest in i.

Block: bare (n = 40; N = 20)

  • a: must 0.80 (0.66–0.94); bare 0.20 (0.06–0.34)
  • d: must 0.68 (0.51–0.85); bare 0.33 (0.16–0.50)
  • i: must 0.78 (0.62–0.93); bare 0.23 (0.07–0.38)

Takeaway: Bare claims a substantial minority share—especially in d—though must remains the plurality across inference conditions.

4.3 Reading Times Summary

5 Experiment 4

5.1 Participant Accuracy in Check Items

gotta vs. must
Total N = 21
Bin Count
[0.7,0.8) 2
[0.9,1] 19
gotta vs. must
Total N = 21
Bin Count
[0.7,0.8) 2
[0.9,1] 19
Click to expand Demographics

Mean Age: 46.00 (35–65)

Subject Age Gender Location Computer Language Other language
S[1] 65 female Arkansas, USA Windows English
S[2] 42 female MO, USA Mac English
S[3] 51 Female California, USA PC English
S[4] 62 male florida, usa pc english
S[5] 43 Female Kansas, USA PC English
S[6] 51 female IL, United States PC English
S[7] 35 Female OH, United States PC English
S[8] 50 male Texas, USA pc English Spanish
S[9] 39 female Willis, TX PC English
S[10] 39 Male Wyoming, USA PC English
S[11] 50 male New Jersey, USA PC English
S[12] 38 female Oklahoma, USA PC English
S[13] 37 Male IL, USA PC English
S[14] 37 Male New Jersey; United States Desktop PC English
S[15] 54 Female Illinois, United States Laptop English
S[16] 48 Male NH PC (windows) English
S[17] 40 Male Maryland, United States PC English
S[18] 43 Male Illinois, USA PC English
S[19] 50 male California, USA pc English Spanish
S[20] 37 Female North Carolina, USA PC English
S[21] 55 Female New York PC English

Mean Age: 50.05 (35–81)

Subject Age Gender Location Computer Language Other language
S[1] 41 female PA, USA PC English
S[2] 38 Male Illinois, USA PC English
S[3] 48 Male Wisconsin, USA PC English
S[4] 59 woman US PC English
S[5] 62 Female California, USA PC English
S[6] 43 male Florida, USA PC English
S[7] 47 Male Georgia, United States PC English
S[8] 51 male NC, Bladen PC English
S[9] 81 Female Tennessee, USA laptop English
S[10] 43 female Michigan, United States PC English
S[11] 44 Male Michigan, United States PC English
S[12] 38 male NC, USA PC English
S[13] 39 Male Kansas, United States PC English
S[14] 55 female Florida, USA PC English
S[15] 53 Woman Ohio, United States Mac English
S[16] 49 male florida, USA PC English
S[17] 53 Woman GA, United States PC Windows English
S[18] 47 Male Indiana, USA PC English
S[19] 65 female North Carolina, USA PC English
S[20] 60 Female MA, USA PC English
S[21] 35 female CA, US Mac English

5.2 Answer Choice Summary

We compare the share of must vs gotta across inference conditions (a, d, i) under two preambles: an if-p conditional (cond) and a well-then discourse preamble (well).

Preamble: if-p (cond)

  • a: must 0.974 (0.924–1.000); gotta 0.026 (0.000–0.076).
  • d: must 0.947 (0.879–1.000); gotta 0.053 (0.000–0.121).
  • i: must 1.000 (1.000–1.000); gotta 0.000.

Takeaway: Near-categorical preference for must under if-p across all inference conditions; gotta contributes only trace amounts in a/d and none in i.

Preamble: well-then (well)

  • a: must 0.947 (0.879–1.000); gotta 0.053 (0.000–0.121).
  • d: must 1.000 (1.000–1.000); gotta 0.000.
  • i: must 0.921 (0.813–1.000); gotta 0.079 (0.000–0.187).

Takeaway: Must still dominates, but well-then allows a small gotta share—most notably in i—while d remains categorically must.

5.3 Reading Times Summary

6 Overall

Preamble age inference Mean Lower CI Upper CI
prob
exp1 If p, ... 22 abductive 0.70 0.42 0.98
exp1 If p, ... 22 deductive 0.30 0.02 0.58
exp1 If p, ... 22 inductive 0.60 0.17 1.00
exp2 Well, then ... 46 abductive 0.54 0.38 0.72
exp2 Well, then ... 46 deductive 0.28 0.13 0.42
exp2 Well, then ... 46 inductive 0.45 0.30 0.60
haveto
exp1 If p, ... 19 abductive 0.07 0.00 0.22
exp1 If p, ... 19 deductive 0.07 0.00 0.22
exp1 If p, ... 19 inductive 0.29 0.07 0.50
exp2 Well, then ... 37 abductive 0.07 0.00 0.17
exp2 Well, then ... 37 deductive 0.29 0.12 0.45
exp2 Well, then ... 37 inductive 0.10 0.00 0.20
exp3 If p, ... 49 abductive 0.07 0.00 0.14
exp3 If p, ... 49 deductive 0.12 0.01 0.23
exp3 If p, ... 49 inductive 0.14 0.05 0.24
will
exp1 If p, ... 22 abductive 0.00 0.00 0.00
exp1 If p, ... 22 deductive 0.20 0.00 0.66
exp1 If p, ... 22 inductive 0.20 0.00 0.48
exp2 Well, then ... 46 abductive 0.05 0.00 0.11
exp2 Well, then ... 46 deductive 0.22 0.08 0.37
exp2 Well, then ... 46 inductive 0.10 0.00 0.21
bare
exp1 If p, ... 21 abductive 0.14 0.00 0.27
exp1 If p, ... 21 deductive 0.09 0.00 0.27
exp1 If p, ... 21 inductive 0.14 0.00 0.27
exp2 Well, then ... 43 abductive 0.22 0.05 0.40
exp2 Well, then ... 43 deductive 0.47 0.28 0.67
exp2 Well, then ... 43 inductive 0.31 0.15 0.46
exp3 If p, ... 49 abductive 0.20 0.06 0.34
exp3 If p, ... 49 deductive 0.32 0.15 0.50
exp3 If p, ... 49 inductive 0.22 0.07 0.38
gotta
exp4 If p, ... 46 abductive 0.03 0.00 0.08
exp4 If p, ... 46 deductive 0.05 0.00 0.12
exp4 If p, ... 46 inductive 0.00 0.00 0.00
exp4 Well, then ... 46 abductive 0.05 0.00 0.12
exp4 Well, then ... 46 deductive 0.00 0.00 0.00
exp4 Well, then ... 46 inductive 0.08 0.00 0.19